Catégorie : Excel function

This function rounds a number down to the nearest multiple of the specified significance value.

Syntax
FLOOR(number; significance)

Arguments

• number (required) – The numeric value to be rounded
• significance (required) – The rounding multiple

Key Behavior:

• Positive numbers: Rounds toward zero (down)
• Negative numbers: Rounds away from zero (up)
• Same sign requirement: Both arguments must be positive or both negative
• Exact multiples: Returns unchanged if number is already a multiple of significance

Error Conditions:

• #VALUE! – Non-numeric arguments
• #NUM! – When number and significance have opposite signs

Examples:

Comparison with Similar Functions:

Function	Direction	Multiple-Based	Handles Negatives
FLOOR	Down	Yes	Yes (with same sign)
CEILING	Up	Yes	Yes
MROUND	Nearest	Yes	Yes
ROUNDDOWN	Down	No	Yes

Applications:

• Price setting and discount calculations
• Time tracking (15-minute increments)
• Inventory management (case quantities)
• Financial reporting (standardized units)

This function returns the double factorial of a specified number, which is the product of all integers with the same parity (odd/even) up to that number.

Syntax
FACTDOUBLE(number)

Argument

• number (required) – A non-negative integer (decimal values are truncated)

Key Properties:

• For even numbers:
  n!! = n × (n-2) × (n-4) × … × 4 × 2
• For odd numbers:
  n!! = n × (n-2) × (n-4) × … × 3 × 1
• Special cases:
  0!! = 1 and 1!! = 1
• Maximum computable value in Excel: FACTDOUBLE(297) for odd, FACTDOUBLE(300) for even

Mathematical Background
Double factorials are used in:

• Advanced combinatorics
• Special function theory
• Quantum physics calculations
• Trigonometric integral solutions

Example Applications:

1. Even Number Example:

=FACTDOUBLE(8) → Returns 384 (8×6×4×2)

1. Odd Number Example:

=FACTDOUBLE(7) → Returns 105 (7×5×3×1)

1. Special Cases:

Formula	Result	Notes
=FACTDOUBLE(0)	1	By definition
=FACTDOUBLE(1)	1
=FACTDOUBLE(5.9)	15	Truncates to 5
=FACTDOUBLE(-1)	#NUM!	Invalid input

Error Conditions:

• #VALUE! – Non-numeric input
• #NUM! – Negative numbers or values exceeding computational limits

Comparison with FACT():

n	FACT(n)	FACTDOUBLE(n)
5	120	15
6	720	48
7	5040	105

Related Functions:

• FACT(): Standard factorial
• MULTINOMIAL(): Generalized factorial
• COMBIN(): Combinatorial calculations

Note: Particularly useful in physics for:

• Normalization constants in quantum mechanics
• Volume calculations in n-dimensional spheres
• Solutions to certain differential equations

This function calculates the factorial of a specified non-negative integer.

Syntax
FACT(number)

Argument

• number (required) – A non-negative integer (decimal values are truncated)

Key Properties:

• For any positive integer n:
  n! = n × (n-1) × (n-2) × … × 2 × 1
• By definition: 0! = 1
• Maximum computable value in Excel: FACT(170) ≈ 7.26E+306
  (Larger values return #NUM! error)

Mathematical Background
Factorials represent:

• Permutations of distinct items
• Partial products of natural numbers
• Fundamental in combinatorics and probability

Example Applications:

1. Race Placement (Permutations)

=FACT(4) → Returns 24

Interpretation: 4 runners can finish in 24 different orders

1. Committee Arrangements

=FACT(5)/FACT(3) → Returns 20 (5P2 permutations)

1. Special Cases:

Formula	Result	Notes
=FACT(0)	1	Definition
=FACT(1)	1
=FACT(5.9)	120	Truncates to 5
=FACT(170)	7.26E+306	Excel’s limit

Error Conditions:

• #VALUE! – Non-numeric input
• #NUM! – Negative numbers or n > 170

This function returns Euler’s number *e* (approximately 2.71828182845904) raised to the power of the specified number.

Syntax
EXP(number)

Argument

• number (required) – The exponent applied to base *e*

Background
The EXP() function performs exponential calculations using:

• Base *e* (Euler’s number), the fundamental constant for natural logarithms
• An irrational, transcendental number (cannot be expressed as a simple fraction)
• The inverse operation of the natural logarithm function LN()

Key Mathematical Properties:

1. Relationship with LN():
   EXP(LN(x)) = x and LN(EXP(x)) = x
2. Special Values:
   • EXP(0) = 1
   • EXP(1) ≈ 2.71828183 (Euler’s number)
3. Growth Characteristics:
   • Models continuous growth/decay processes
   • Fundamental in calculus (derivative of EXP(x) is EXP(x))

Examples:

1. Basic Calculations:

=EXP(1) → Returns 2.71828183 (e)

=EXP(2) → Returns 7.3890561 (e²)

=EXP(0) → Returns 1

1. Scientific Applications:
   • Radioactive decay: =EXP(-decay_constant*time)
   • Population growth: =initial_population*EXP(growth_rate*time)
2. Financial Modeling:

=principal*EXP(rate*years)  // Continuous compounding

Comparison with Power Operator (^):

Method	Example	Result
EXP()	=EXP(1)	e (2.718…)
^	=2.71828182845904^1	e (2.718…)
^	=2^8	256 (different base)

Common Uses:

• Continuous growth/decay models
• Probability distributions
• Complex number calculations
• Differential equations solutions
• Financial continuous compounding

Note: For exponents with different bases, use the caret operator (^):

=base^exponent

This function rounds a specified number up to the nearest even integer.

Syntax
EVEN(number)

Argument

• number (required) – The numeric value to be rounded
  • Must be a numeric expression
  • Returns #VALUE! error for non-numeric inputs

Background
The EVEN() function performs rounding differently than standard rounding functions:

• Always rounds away from zero to the next even integer
• Maintains the sign of the original number
• Returns the input value unchanged if it is already an even integer
• Follows mathematical definition of even numbers (integers divisible by 2)

Key Characteristics:

• Rounding direction:
  • Positive numbers: rounds up to next even integer
  • Negative numbers: rounds down to next even integer (more negative)
• Special cases:
  • Zero (0) is considered even and returns 0
  • Exact even integers return themselves

Examples:

Applications:

• Financial calculations requiring even denominations
• Inventory management for paired items
• Team/group formation requiring even numbers
• Data processing with even-number constraints

Error Conditions:

• #VALUE! – Non-numeric input
• #NUM! – Extremely large numbers (Excel limitation)

Related Functions:

• ODD(): Rounds to nearest odd integer
• CEILING(): Rounds to specified multiple
• FLOOR(): Rounds down to specified multiple

Its converts an angle from radians to degrees.

Syntax
DEGREES(angle)

Argument

• angle (required) – The angle in radians to be converted

Background
Angular measurements use two primary units:

1. Degrees (°):
   • Full circle = 360°
   • 1° = 60 arcminutes (‘)
   • 1′ = 60 arcseconds (« )
2. Radians:
   • Full circle = 2π radians
   • π radians = 180°
   • 1 radian ≈ 57.2958°

Key Features:

• Essential for interpreting results from Excel’s trigonometric functions (ACOS, ASIN, ATAN, etc.)
• Conversion formula:

degrees=radians×180π

• Inverse function: RADIANS() converts degrees to radians

Examples:

Applications:

• Converting mathematical/engineering calculations to more intuitive degree measurements
• Preparing data for visual presentations/graphs
• Geographic coordinate transformations
• CAD/CAM software inputs

This function returns the hyperbolic cosine of a number.

Syntax
COSH(number)

Argument

• number (required) – Any real number

Background
The hyperbolic cosine is part of the family of hyperbolic functions, which – like trigonometric functions – are defined for all real and complex numbers (though Excel only supports real-number arguments). The function is mathematically defined as:

The graph of the hyperbolic cosine (shown in Figure below) displays a characteristic curve.

Example Calculation

Key Applications

1. Catenary Curves
   The hyperbolic cosine famously describes the shape of a hanging chain or cable suspended between two points (catenary). The catenary equation is:

y = a * COSH(x/a)

where:

1. • a is the vertical distance from the lowest point to the baseline
   • x is the horizontal coordinate
2. Scientific Uses
   • Engineering analysis (suspension bridges, arches)
   • Physics (relativity and wave equations)
   • Mathematical modeling

Technical Notes

• Output is always ≥ 1
• Symmetric function: COSH(-x) = COSH(x)
• Grows exponentially as |x| increases
• Fundamental relationship: COSH²x – SINH²x = 1

This function returns the cosine of the specified angle.

Syntax
COS(number)

Argument

• number (required) – The angle in radians for which you want to calculate the cosine

Background
The cosine of an angle in a right triangle represents the ratio of the length of the adjacent side to the hypotenuse (see Figure below):

cos(α) = adjacent side / hypotenuse

Key Properties:

• For a unit circle (radius = 1), as angle α increases from 0° to 90°:
  • cos(α) decreases from 1 to 0 (see Figure below)

• The cosine function produces a wave-like curve when plotted on a coordinate system (see Figure below)

• The function expects the input angle in radians
• To convert degrees to radians, use the RADIANS() function

Example Application

Additional Notes:

• The cosine function is periodic with a period of 2π radians (360°)
• cos(0) = 1
• cos(π/2) = 0 (90°)
• cos(π) = -1 (180°)
• cos(3π/2) = 0 (270°)
• cos(2π) = 1 (360°)

Common Applications:

• Engineering calculations
• Physics problems involving waves and oscillations
• Computer graphics and game development
• Navigation systems

This function calculates the number of possible combinations (unordered groups) that can be formed from a given set of items.

Syntax
COMBIN(number; number_chosen)

Arguments

• number (required) – Total items in the set (must be ≥ 0)
• number_chosen (required) – Items to select in each combination (must be ≥ 0 and ≤ number)

Key Features:

• Returns the binomial coefficient « n choose k »
• Mathematically represented as:

n! / (k!(n-k)!)

• Truncates decimal inputs to integers
• Combination order doesn’t matter (AB = BA)

Error Conditions:

• #VALUE! – Non-numeric arguments
• #NUM! – If:
  • Either argument is negative
  • number < number_chosen
  • Arguments exceed computation limits

Examples:

=COMBIN(4;2) → Returns 6 possible matches

Comparison with PERMUT():

Function	Order Matters	Formula	Example (4,2)
COMBIN	No	n!/(k!(n-k)!)	6
PERMUT	Yes	n!/(n-k)!	12

Applications:

• Probability calculations
• Tournament scheduling
• Statistical analysis
• Combinatorial mathematics
• Quality control sampling

Note: For large numbers (n > 170), consider alternative methods due to Excel’s factorial computation limits.

This function rounds a number up to the nearest multiple of the specified significance value.

Syntax
CEILING(number; significance)

Arguments

• number (required) – The numeric value you want to round
• significance (required) – The multiple to which you want to round

Key Features:

• Always rounds numbers away from zero
• Handles both positive and negative numbers:
  • Positive numbers round up (e.g., 3.2 → 4)
  • Negative numbers round down (e.g., -3.2 → -4)
• Returns original value if already an exact multiple
• Returns errors for:
  • Non-numeric inputs (#VALUE!)
  • Mixed signs between arguments (#NUM!)

Example:

Comparison with Similar Functions:

Function	Direction	Multiple-Based	Handles Negatives
CEILING	Up (from zero)	Yes	Yes
FLOOR	Down (toward zero)	Yes	Yes
MROUND	Nearest	Yes	Yes
ROUNDUP	Up	No	Yes